For pt.I see ibid., vol.16, p.545-58 (1990). A procedure for canonical field quantisation on a non-orthogonal basis is proposed. It is used to quantise the quark-gluon fields in a bag enclosed by its moving surface. The self-consistency of this procedure is proven by finding an invariant in each case. Feynman rules for interacting quark-gluon systems are given.